UoH 2021 Question 17: Real analysis

Consider an economy with 2-goods. The set of all possible positive relative prices is given as: $P = \{(p_1, p_2) \mid p_1, p_2 > 0,\ \text{and } p_1 + p_2 = 1\}$. Identify the correct statements about the properties of set $P$:

I. $P$ is convex. II. $P$ is bounded. III. $P$ is closed. IV. $P$ is compact. V. $P$ is empty.